Real‐time direct kinematics of general six‐degree‐of‐freedom parallel manipulators with minimum‐sensor data

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Abstract
We present a formulation of the direct kinematics of a general six‐degree‐of‐freedom parallel manipulator, sometimes referred to as the generalized Steward platform, whereby the positioning and orientation problems are decoupled by introducing two auxiliary coordinates in the forms of either two angles or two lengths. This is in accordance with the type of extra sensors, i.e., rotary or translational, that are collocated on a leg of the manipulator. Moreover, a real‐time implementation of extra‐sensor data, with a unique direct kinematics solution, is proposed by resorting to an eigenvalue problem. The parallelism in the proposed formulation enables the user to benefit from a parallel computing environment. Hence, we introduce a parallel computing algorithm that highly increases the robustness of the computational algorithm. © 1995 John Wiley & Sons, Inc.

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